Problem: The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $$6.50$, and bags of cookies cost $$4.00$, and sales equaled $$54.00$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the drama club.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+4y = 54}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${6.5x + 4}{(x+3)}{= 54}$ Simplify and solve for $x$ $ 6.5x+4x + 12 = 54 $ $ 10.5x+12 = 54 $ $ 10.5x = 42 $ $ x = \dfrac{42}{10.5} $ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(4)}{ + 3}$ ${y = 7}$ You can also plug ${x = 4}$ into $ {6.5x+4y = 54}$ and get the same answer for $y$ ${6.5}{(4)}{ + 4y = 54}$ ${y = 7}$ $4$ bags of candy and $7$ bags of cookies were sold.